use the graph shown to answer the question. g...
use the graph shown to answer the question. growth curve a represents $200 saved at 2.5 percent simple interest. growth curve b represents $200 saved at 2.5 percent interest, compounded quarterly. what is the approximate difference between the two accounts in 20 years? $100 $50 $25 $10
Answer
# Explanation:
## Step1: Calculate simple - interest amount
The simple - interest formula is $A = P(1+rt)$, where $P=\$200$, $r = 0.025$ (2.5% as a decimal), and $t = 20$ years.
$A_{s}=200(1 + 0.025\times20)=200(1 + 0.5)=200\times1.5=\$300$
## Step2: Calculate compound - interest amount
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P = 200$, $r=0.025$, $n = 4$ (compounded quarterly), and $t = 20$ years.
$A_{c}=200(1+\frac{0.025}{4})^{4\times20}=200(1 + 0.00625)^{80}$.
Let $x=(1 + 0.00625)^{80}$. Using the formula $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$, or simply using a calculator, $x\approx1.640605$.
So $A_{c}=200\times1.640605=\$328.121$.
## Step3: Calculate the difference
$D=A_{c}-A_{s}=328.121 - 300=\$28.121\approx\$25$.
# Answer:
$25$